Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉
© 2019 Elsevier B.V. Let R=GR(pe,m)[u]∕〈uk〉 be a finite commutative ring for a prime p and any positive integers e,m and k. In this paper, we derive the explicit representation of cyclic codes over the ring R of length n, where n and p are coprime. We also discuss the dual of such cyclic codes over...
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| Main Authors: | , , , |
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| Format: | Journal |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85068585212&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/65704 |
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| Institution: | Chiang Mai University |
| Summary: | © 2019 Elsevier B.V. Let R=GR(pe,m)[u]∕〈uk〉 be a finite commutative ring for a prime p and any positive integers e,m and k. In this paper, we derive the explicit representation of cyclic codes over the ring R of length n, where n and p are coprime. We also discuss the dual of such cyclic codes over the ring R and give a sufficient condition for the codes to be self-dual. Moreover, we study quasi-cyclic codes of length kn and index k over the ring R, and obtain some good codes satisfying the bound given in Dougherty and Shiromoto (2000) over the ring Z9 as an example. |
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